Physical And Numerical Models In Knot Theory

Including Applications To The Life Sciences

By: Andrzej Stasiak (Editor), Kenneth C Millett (Editor), Jorge Alberto Calvo (Editor), Eric J Rawdon (Editor)

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Hardcover | 21 September 2005

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628 Pages

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The physical properties of knotted and linked configurations in space have been of interest to physicists and mathematicians for a long time. More recently and more widely, they have become interesting to biological and computer scientists, and to engineers among others. The depth of importance and breadth of application are now widely appreciated. In this volume, there are several contributions from researchers who are using computers to study problems that would otherwise be untractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. From properties of knot invariants, to knot tabulation, studies of hyperbolic structures, knot energies, and to the exploration of spaces of knots, computers have opened the doors to problems that would have otherwise been too difficult to do by hand computation. There are also contributions concentrating on models that researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics range from knotted umbilical cords, to studies of DNA knots and knots in proteins.

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Non-Fiction Mathematics Topology Algebraic Topology Science Biology, Life Sciences Molecular Biology Geometry Analytic Geometry Booktopia Publisher Services World Scientific Publishing

Preface	p. vii
On the Theory of Solid Knots	p. 1
A Tutorial on Knot Energies	p. 19
Universal Energy Spectrum of Tight Knots and Links in Physics	p. 45
Knot Dynamics in a Driven Hanging Chain: Experimental Results	p. 65
Biarcs, Global Radius of Curvature, and the Computation of Ideal Knot Shapes (4 color plates)	p. 75
Knotted Umbilical Cords (2 color plates)	p. 109
Modelling DNA as a Flexible Thick Polymer: DNA Elasticity and Packaging Thermodynamics	p. 127
Monte-Carlo Simulations of Gel-Electrophoresis of DNA Knots	p. 149
Atomic Force Microscopy of Complex DNA Knots	p. 161
Protein Folds, Knots and Tangles	p. 171
Tying Down Open Knots: A Statistical Method for Identifying Open Knots with Applications to Proteins (7 color plates)	p. 203
Scaling of the Average Crossing Number in Equilateral Random Walks, Knots and Proteins	p. 219
Folding Complexity in a Random-Walk Copolymer Model	p. 233
Universal Characteristics of Polygonal Knot Probabilities	p. 247
The Average Crossing Number of Gaussian Random Walks and Polygons	p. 275
Ropelength of Tight Polygonal Knots	p. 293
A Fast Octree-Based Algorithm for Computing Ropelength	p. 323
Topological Entropic Force between a Pair of Random Knots Forming a Fixed Link	p. 343
Under-Knotted and Over-Knotted Polymers: 1. Unrestricted Loops	p. 363
Under-Knotted and Over-Knotted Polymers: 2. Compact Self-Avoiding Loops	p. 385
On the Mean Gyration Radius and the Radial Distribution Function of Ring Polymers with Excluded Volume under a Topological Constraint	p. 399
Thermodynamics and Topology of Disordered Knots. Correlations in Trivial Lattice Knot Diagrams	p. 421
Generating Large Random Knot Projections	p. 473
Minimal Flat Knotted Ribbons	p. 495
Quadrisecants of Knots with Small Crossing Number	p. 507
On the Writhing Number of a Non-Closed Curve	p. 525
On a Mathematical Model for Thick Surfaces	p. 547
Some Ropelength-Critical Clasps	p. 565
Remarks on Some Hyperbolic Invariants of 2-Bridge Knots	p. 581
Conjectures on the Enumeration of Alternating Links	p. 597
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Physical And Numerical Models In Knot Theory

Including Applications To The Life Sciences

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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